The present invention relates to a film thickness measuring apparatus for measuring a film thickness. More particularly, the present invention relates to a film thickness measuring method and a film thickness measuring apparatus in which light is projected onto a film to be measured, and reflected light from the film is received to measure the thickness of the film based on the intensity of the reflected light. It should be noted that the term xe2x80x9cfilm thickness measurementxe2x80x9d as used in this specification includes not only the measurement of a film thickness but also the detection of a substrate condition, for example, as to whether or not a metal film is present on a substrate, or the observation of a substrate condition.
There has heretofore been a film thickness measuring apparatus in which light is applied to a film under measurement, and reflected light from the upper and lower interface surfaces of the film is received. The thickness of the film is measured by making use of the phenomenon that light reflected from the upper and lower interface surfaces of the film interfere with each other, and the reflected light intensity changes according to the thickness of the film.
FIGS. 1 and 2 are flowcharts showing the process for calculating a film thickness based on the intensity of reflected light received in a conventional film thickness measuring apparatus of the type described above. To calculate a film thickness, as shown in FIG. 1, a spectral reflectance ratio S(xcex) is determined (see curve a in FIG. 3) from the spectral reflection intensity at a measuring point (a spot where the film under measurement is present) (step ST1). In addition, a spectral reflectance ratio R(xcex) is determined (see curve b in FIG. 3) from the spectral reflection intensity at a spot where the film under measurement is not present (step ST2). The spectral reflectance ratio S(xcex) is divided by the spectral reflectance ratio R(xcex) to obtain a spectral reflectance ratio (=measured profile) Rmeas(xcex)=S(xcex)/R(xcex) of the film (see curve c in FIG. 3) (step ST3). It should be noted that curves a and b in FIG. 3 show a case where the wavelength xcex spectrum of reflected light is continuous when a halogen lamp is used as an incident light source, for example.
To determine a film thickness value D, a variable d is used to represent the film thickness, and d is changed in a range (from d1 to d2) where the proper film thickness value is expected to be present. First, d is initialized (d=d1) (step ST4), and an evaluation value Ed is determined from the square-sum of differences between the theoretical value Rcalc(xcex) and the measured value Rmeas(xcex) of the spectral reflectance ratio at the relevant film thickness d to obtain an evaluation function E(d) (step ST5). A minimum unit (d of measurement is added to the film thickness d (d=d+xcex94d) (step ST6). Subsequently, it is determined whether or not dxe2x89xa6d2 (step ST7). If dxe2x89xa6d2, the process returns to step ST5 to repeat the processing. If dxe2x89xa6d2 does not hold, the film thickness d that gives a minimum value of the evaluation function E(d) is determined to be a measured film thickness value D (step ST8).
FIG. 2 is a flowchart showing the processing for determining an evaluation value Ed from the square-sum of differences between the theoretical value Rcalc(xcex) and the measured value Rmeas(xcex) of the spectral reflectance ratio in the measuring wavelength range (from xcex1 to xcex2) at the relevant film thickness d at the above-described step ST5 to obtain an evaluation function E(d). First, initialization is executed (xcex=xcex1, Ed=0) to change the wavelength xcex within the measuring wavelength range of from xcex1 to xcex2 (step ST11).
Next, an evaluation value Ed is determined by the following calculation (step ST12). The square-sum of differences between the theoretical value Rcalc(xcex) and the measured value Rmeas(xcex) at the relevant film thickness is determined.
Excex=(Rmeas(xcex)xe2x88x92Rcalc(xcex))2
Ed=Ed+Excex
When the absorption coefficient is assumed to be zero, the theoretical value Rcalc(xcex) can be calculated from the following equation:
xe2x80x83Rcalc(xcex)=r12+r22+2xc3x97r1xc3x97r2xc3x97cos xcex4
where r1=(1xe2x88x92n1)/(1+n1); r2=(1xe2x88x92nb)/(1+nb); xcex4=4xcfx80n1 d/xcex; n1 is the refractive index of the film; nb is the refractive index of the substrate; d is the film thickness; and xcex is the measuring wavelength range (from xcex1 to xcex2).
Next, the resolution xcex94xcex in the direction of the measuring wavelength range is added (xcex=xcex+xcex94xcex) (step ST13). Subsequently, it is determined whether or not xcexxe2x89xa6xcex2 (step ST14). If, xcexxe2x89xa6xcex2 the process returns to step ST12 to repeat the processing. If xcexxe2x89xa6xcex2 does not hold, the evaluation value Ed is substituted into the evaluation function E(d) (E(d)=Ed) (step ST15). Then, the process proceeds to step ST6 in FIG. 1.
Thus, the conventional process for calculating a film thickness is as follows. To obtain a spectral reflectance ratio (=measured profile) of a film under measurement, the spectral reflection intensity at a measuring point is measured, and the spectral reflection intensity for calibration (at a spot where the film under measurement is not present) is measured. Then, the former spectral reflection intensity is divided by the latter spectral reflection intensity to obtain a spectral reflectance ratio of the film. The measured profile thus obtained is compared with a theoretically calculated spectral reflectance ratio based on an assumed film thickness, and an assumed film thickness that gives a minimum difference between the measured profile and the theoretically calculated spectral reflectance ratio is determined to be a measured film thickness.
For this type of conventional film thickness measuring apparatus, mechanical and optical schemes have been devised with an emphasis on how a measured profile is obtained accurately with a good S/N ratio by optical or other techniques meeting a demand for high accuracy. Accordingly, the spectral reflection intensity obtained from the film to be measured provides a sufficiently high intensity to obtain the desired result. Therefore, the film thickness can be measured satisfactorily by an algorithm in which the measured profile and the theoretically calculated spectral reflectance ratio are compared directly to each other as stated above.
However, in a thin-film processing apparatus such as a chemical/mechanical polishing apparatus (CMP) for chemically and mechanically polishing substrates, e.g. semiconductor wafers, there has recently been an increasing demand for measurement inside the thin-film processing apparatus and measurement during processing. In this case, a film thickness measuring apparatus must be installed without interfering with polishing or other processing for which the processing apparatus is designed. In addition, because the measurement of film thickness is an accessory function, the film thickness measuring apparatus is required to be simplified in structure with a view to minimizing costs. In other words, in the measurement of a film thickness carried out inside the thin-film processing apparatus or during processing, it is difficult to detect a sufficiently high spectral reflection intensity to obtain the desired result, which has heretofore been possible to attain without any problem.
FIGS. 3 to 6 are diagrams showing measured data concerning a SiO2 film with a thickness of about 460 nanometers (nm) provided on a silicon (Si) substrate. FIGS. 3 and 4 are diagrams showing measured data in a case where the spectral reflection intensity is sufficiently high to obtain a film thickness value. Curves a, b and c in FIG. 3 are the spectral reflectance ratios S(xcex), R(xcex) and the measured profile Rmeas(xcex)=S(xcex)/R(xcex), respectively, determined at steps ST1, ST2 and ST3 in FIG. 1. Curve e in FIG. 4 is the evaluation function E(d) obtained at step ST5 in FIG. 1.
FIGS. 5 and 6 are diagrams showing measured data in a case where the spectral reflection intensity is not sufficiently high to obtain the desired result. Curves a, b and c in FIG. 5 are the spectral reflectance ratios S(xcex), R(xcex) and the measured profile Rmeas(xcex)=S(xcex)/R(xcex), respectively, determined at steps ST1, ST2 and ST3 in FIG. 1. Curve e in FIG. 6 is the evaluation function E(d) obtained at step ST5 in FIG. 1.
In FIGS. 3 and 4, d that gives a minimum value of the evaluation function E(d) shows an accurate film thickness value (460 nanometers). However, in FIGS. 5 and 6, d that gives a minimum value of the evaluation function E(d) does not show an accurate film thickness value.
Some film thickness measuring apparatuses are used to measure a film thickness during polishing or other processing and to detect an end point of such processing. There are demands for such film thickness measuring apparatuses to obtain a measurement result at high speed and in real time. The conventional film thickness measuring apparatus cannot satisfactorily meet the demands.
The present invention was made in view of the above-described circumstances. An object of the present invention is to provide a film thickness measuring method and a film thickness measuring apparatus capable of measuring a film thickness with high accuracy even if the spectral reflection intensity is not sufficiently high to measure an accurate film thickness and gives a poor S/N ratio.
To attain the above-described object, the present invention provides a film thickness measuring method wherein light is applied to a film under measurement, and reflected light from the upper and lower interface surfaces of the film is received to measure the thickness of the film. According to the film thickness measuring method, a spectral reflectance ratio S(xcex) at a spot where the film under measurement is present is measured by using light of a plurality of different wavelengths xcex(xcex1xe2x89xa6xcexxe2x89xa6xcex2; a measuring wavelength range), and a spectral reflectance ratio R(xcex) at a spot where the film under measurement is not present is measured by using the light of a plurality of different wavelengths to determine a measured spectral reflectance ratio Rmeas(xcex)=S(xcex)/R(xcex). A theoretical value Rcalc(xcex) of a spectral reflectance ratio at an assumed film thickness d is determined, and an evaluation value Ed is determined from the square-sum of differences between the measured spectral reflectance ratio Rmeas(xcex) and the theoretical value Rcalc(xcex) of spectral reflectance ratio at the film thickness d according to the following equation:   Ed  =            ∑              λ        =                  λ          ⁢                      xe2x80x83                    ⁢          1                            λ        ⁢                  xe2x80x83                ⁢        2              ⁢          xe2x80x83        ⁢                  (                              Rmeas            ⁡                          (              λ              )                                -                      Rcalc            ⁡                          (              λ              )                                      )            2      
The film thickness d is changed (increased or decreased) in steps of (d in a measuring retrieval range of from d1 to d2 to determine an evaluation value Ed at each relevant film thickness, thereby obtaining an evaluation function E(d) with respect to the film thickness d. Assuming that the spectral reflectance ratio Rmeas(xcexe) of the film is 1 (Rmeas(xcexe)=1), an evaluation value Enewd is determined from the square-sum of differences between a theoretical value Rcalc(xcexe) of spectral reflectance ratio at a certain film thickness d and the spectral reflectance ratio Rmeas(xcexe)=1 according to the following equation:   Enewd  =            ∑                        λ          ⁢                      xe2x80x83                    ⁢          e                =                  λ          ⁢                      xe2x80x83                    ⁢          1                            λ        ⁢                  xe2x80x83                ⁢        2              ⁢          xe2x80x83        ⁢                  (                              Rcalc            ⁡                          (                              λ                ⁢                                  xe2x80x83                                ⁢                e                            )                                -          1                )            2      
The film thickness d is changed (increased or decreased) in steps of xcex94d in a measuring retrieval range of from d1 to d2 to determine an evaluation value Enewd at each relevant film thickness, thereby obtaining an evaluation function Enew(d). A ratio PE(d) of the evaluation function E(d) to the evaluation function Enew(d) is determined (PE(d)=E(d)/Enew(d)), and a film thickness d that gives a minimum value of the evaluation function ratio PE(d) is determined to be a measured film thickness value D.
In addition, the present invention provides a film thickness measuring apparatus including an optical system for applying light to a film under measurement and for receiving and dispersing reflected light from the upper and lower interface surfaces of the film. The film thickness measuring apparatus further includes a film thickness measuring device for measuring the thickness of the film from the intensity of reflected light received with the optical system. The film thickness measuring device includes a computing unit for executing the following processing: A spectral reflectance ratio S(xcex) at a spot where the film under measurement is present is measured by using light of a plurality of different wavelengths xcex(xcex1xe2x89xa6xcexxe2x89xa6xcex2; a measuring wavelength range), and a spectral reflectance ratio R(xcex) at a spot where the film under measurement is not present is measured by using the light of a plurality of different wavelengths to determine a measured spectral reflectance ratio Rmeas(xcex)=S(xcex)/R(xcex). A theoretical value Rcalc(xcex) of spectral reflectance ratio at an assumed film thickness d is determined, and an evaluation value Ed is determined from the square-sum of differences between the measured spectral reflectance ratio Rmeas(xcex) and the theoretical value Rcalc(xcex) of spectral reflectance ratio at the film thickness d according to the following equation:   Ed  =            ∑              λ        =                  λ          ⁢                      xe2x80x83                    ⁢          1                            λ        ⁢                  xe2x80x83                ⁢        2              ⁢          xe2x80x83        ⁢                  (                              Rmeas            ⁡                          (              λ              )                                -                      Rcalc            ⁡                          (              λ              )                                      )            2      
The film thickness d is changed (increased or decreased) in steps of xcex94d in a measuring retrieval range of from d1 to d2 to determine an evaluation value Ed at each relevant film thickness, thereby obtaining an evaluation function E(d) with respect to the film thickness d. Assuming that the spectral reflectance ratio Rmeas(xcexe) of the film is 1 (Rmeas(xcexe)=1), an evaluation value Enewd is determined from the square-sum of differences between a theoretical value Rcalc(xcexe) of spectral reflectance ratio at a certain film thickness d and the spectral reflectance ratio Rmeas(xcexe)=1 according to the following equation:   Enewd  =            ∑                        λ          ⁢                      xe2x80x83                    ⁢          e                =                  λ          ⁢                      xe2x80x83                    ⁢          1                            λ        ⁢                  xe2x80x83                ⁢        2              ⁢          xe2x80x83        ⁢                  (                              Rcalc            ⁡                          (                              λ                ⁢                                  xe2x80x83                                ⁢                e                            )                                -          1                )            2      
The film thickness d is changed (increased or decreased) in steps of (d in a measuring retrieval range of from d1 to d2 to determine an evaluation value Enewd at each relevant film thickness, thereby obtaining an evaluation function Enew(d). A ratio PE(d) of the evaluation function E(d) to the evaluation function Enew(d) is determined (PE(d)=E(d)/Enew(d)), and a film thickness d that gives a minimum value of the evaluation function ratio PE(d) is determined to be a measured film thickness value D.
Thus, the film thickness measuring method and apparatus according to the present invention obtains an evaluation function Enew(d) of the theoretical value Rcalc(xcexe) of spectral reflectance ratio and the spectral reflectance ratio of the film under measurement as assumed to be S(xcexe)/R(xcexe)=1 for each wavelength xcex in the measuring range of the film thickness d. The evaluation function E(d) is divided by the evaluation function Enew(d) (E(d)/Enew(d)) to determine a ratio PE(d) between the evaluation functions, which is a signal component attributable to the proper film thickness, and a film thickness d that gives a minimum value of the ratio PE(d) is decided to be a measured film thickness value D. Accordingly, it is possible to perform film thickness measurement of high accuracy even if the spectral reflection intensity is not sufficiently high to measure an accurate film thickness and gives a poor S/N ratio, as stated later in detail.